Capacitor Bank Calculator
How the formula works
The calculator finds the reactive power needed to reach the target power factor, corrects it for capacitor voltage and reactor, then divides the bank into equal steps.
Formulas
Required kVAr = kW × (tan φ1 − tan φ2), where φ = acos(power factor)
Factor k = (System voltage / Capacitor rated voltage)² / (1 − Reactor %)
Nameplate kVAr needed = Required kVAr / k
Number of steps = Nameplate kVAr / Step size (rounded up)
Net kVAr = Installed nameplate kVAr × k
New power factor = cos(atan(tan φ1 − Net kVAr / kW))
Capacitor current = Net kVAr × 1000 / (√3 × V)
Where:
- pf1 = existing power factor, pf2 = target power factor
- A capacitor rated above the system voltage gives less kVAr at the system voltage
- A detuned reactor raises the capacitor voltage, so a higher rated capacitor is needed
Typical values
Target power factor: 0.95 to 0.99. Capacitor rated voltage: 440 V, 480 V or 525 V for a 415 V system (525 V is common with detuned reactors). Detuned reactors: 5.67 % (about 210 Hz), 7 % (about 189 Hz) and 14 % (about 134 Hz). Common step sizes: 5, 10, 12.5, 15, 20, 25, 30, 40 and 50 kVAr. Non-linear load share: below 15 % low, 15 to 25 % medium, above 25 % high. These are typical planning values in line with common IEC practice. The capacitor maker’s data and the local code are final.
How to use the calculator: enter the load and power factors, choose voltage, rated voltage, reactor and step size, then click Calculate.
Important notes: harmonics can cause resonance with plain capacitors. A harmonic study is advised when non-linear load is high.
Worked example
Example 1: Factory load, Auto step
250 kW, power factor 0.75 to 0.95, 415 V, capacitor rated 415 V, no reactor.
Required kVAr = 250 × (0.8819 − 0.3287) = 138.3 kVAr. Auto step gives 12 × 12.5 kVAr = 150 kVAr. New power factor = 0.962. Current falls from 463.7 A to 366.1 A.
Example 2: 440 V capacitors on a 415 V system
100 kW, 0.80 to 0.98, 10 kVAr steps.
Required = 54.7 kVAr. Factor k = (415 / 440)² = 0.890. Nameplate needed = 61.5 kVAr. Use 7 × 10 kVAr = 70 kVAr nameplate, which gives 62.3 kVAr net. New power factor = 0.992.
Example 3: 7 % detuned bank
500 kW, 0.70 to 0.97, 415 V system, 525 V capacitors, 7 % reactor, 50 kVAr steps.
Required = 384.8 kVAr. Capacitor voltage with reactor = 446 V. Factor k = 0.672. Nameplate needed = 572.7 kVAr. Use 12 × 50 kVAr = 600 kVAr nameplate, which gives 403.1 kVAr net. New power factor = 0.978.
Example 4: Small workshop
40 kW, 0.85 to 0.99, 400 V, 5 kVAr steps.
Required = 19.1 kVAr. Use 4 × 5 kVAr = 20 kVAr. New power factor = 0.993.
Example 5: Unity power factor target
60 kW, 0.90 to 1.00, 415 V, 10 kVAr steps.
Required = 29.1 kVAr. Use 3 × 10 kVAr = 30 kVAr. The result is a power factor of 1.000, slightly leading, so check for over-correction at light load.
Common mistakes
- Using the full connected load instead of the average or maximum demand kW.
- Using the wrong existing power factor, for example a nameplate value instead of the measured value.
- Choosing a capacitor rated at a higher voltage but not allowing for the lower kVAr output.
- Installing plain capacitors on a system with a high share of non-linear loads such as drives and UPS.
- Using a detuned reactor with a capacitor whose rated voltage is too low.
- Selecting steps that are too large, so the bank over-corrects at light load.
- Targeting a power factor of 1.00, which can lead to leading power factor.
- Forgetting that capacitor kVAr falls when the system voltage is low.
- Ignoring the capacitor current when sizing cable, contactor and fuse.
Frequently asked questions
How do I select a capacitor bank?
Find the required kVAr from the load and the power factors, correct it for voltage and reactor, then divide it into standard steps.
What is the formula for kVAr?
kVAr = kW × (tan φ1 − tan φ2), where φ is the angle of the power factor.
What is an APFC panel?
An automatic power factor correction panel switches capacitor steps on and off to keep the power factor near the target.
What step size should I choose?
Smaller steps give finer control but need more contactors. Many panels use 6 to 12 steps.
Why use a 440 V or 525 V capacitor on a 415 V system?
A higher rated capacitor handles voltage rise and harmonics better, but gives less kVAr at 415 V.
What is a detuned reactor?
It is a reactor in series with the capacitor. It moves the resonance point below the main harmonics to protect the capacitor.
Which reactor percentage should I use?
7 % is the most common. 5.67 % suits lower 3rd harmonic risk, and 14 % suits a strong 3rd harmonic.
Can I use plain capacitors?
Yes, when non-linear load is low. With drives, UPS or LED loads, detuned banks are safer.
What target power factor is best?
0.95 to 0.99 is common. Some utilities give an incentive above 0.95. Avoid going leading.
What happens if I over-correct?
The power factor becomes leading, voltage can rise and the utility may charge a penalty.
How is capacitor current calculated?
Capacitor current = kVAr × 1000 / (√3 × V) for a three phase bank.
Is this a final design?
No. It is a preliminary selection. Final design should follow the capacitor maker’s data and the local code.